Information Properties of Boundary Line Models for N2O Emissions from Agricultural Soils
Abstract
:1. Introduction
2. Models and Data
2.1. Boundary Line Models
2.2. Data
Forecast category, fi | Observed category, oj | Row sums | ||
---|---|---|---|---|
1. Low | 2. Medium | 3. High | ||
1. Low | 0.2841 | 0.0554 | 0.0074 | 0.3469 |
2. Medium | 0.1181 | 0.1513 | 0.0959 | 0.3653 |
3. High | 0.0480 | 0.0812 | 0.1587 | 0.2878 |
Column sums | 0.4502 | 0.2878 | 0.2620 | 1.0000 |
3. Analysis of Information Properties
3.1. Information Content
3.2. Expected Mutual Information
3.2.1. The G2-test
3.2.2. Conditional Entropy
3.2.3. Normalized Mutual Information
3.3. Specific Information
3.4. Relative Entropy
3.5. A Second Data Set
Forecast category, fi | Observed category, oj | Row sums | ||
---|---|---|---|---|
1. Low | 2. Medium | 3. High | ||
1. Low | 0.7854 | 0.0324 | 0.0000 | 0.8178 |
2. Medium | 0.0972 | 0.0445 | 0.0040 | 0.1457 |
3. High | 0.0121 | 0.0202 | 0.0040 | 0.0364 |
Column sums | 0.8947 | 0.0972 | 0.0081 | 1.0000 |
Information quantity | Equation (boldface indicates equation used for calculation) | Value (nits) for pasture and sugarcane soils data (Table 1) | Value (nits) for cereal cropping soils data (Table 2) |
---|---|---|---|
H(O) | 1 | 1.0687 | 0.3650 |
H(F) | 2 | 1.0936 | 0.5659 |
H(O,F) | 3 | 1.9585 | 0.8430 |
IM(O,F) | 4, 5, 6, 7, 12, 16, 17 | 0.2038 | 0.0879 |
H(O|F) | Component of 6 | 0.8649 | 0.2772 |
H(F|O) | Component of 7 | 0.8898 | 0.4780 |
normalized IM(O,F) | 8 | 0.1907 | 0.2407 |
H(O|f1) | 9 | 0.5382 a,b | 0.1667 |
H(O|f2) | 9 | 1.0813 a,b | 0.7321 |
H(O|f3) | 9 | 0.9839 a,b | 0.9369 |
IS(f1) | 10, 11 | 0.5305 a | 0.1984 |
IS(f2) | 10, 11 | −0.0126 a | −0.3671 |
IS(f3) | 10, 11 | 0.0848 a | −0.5718 |
I(f1) | 15 | 0.3428 b | 0.0325 |
I(f2) | 15 | 0.0442 b | 0.1882 |
I(f3) | 15 | 0.2388 b | 0.9305 |
4. Results and Discussion
- for cereal cropping soils, information properties of the three sub-region model largely depend on the prior (i.e., pre-forecast) probabilities Pr(o1) (≈0.9), Pr(o2) (≈0.1) and Pr(o3) (<0.01) of the observed N2O flux categories o1 (‘low’), o2 (‘medium’) and o3 (‘high’) respectively;
- for pasture and sugarcane soils, information properties of the three sub-region model indicate that observed N2O flux categories o1 (‘low’), o2 (‘medium’) and o3 (‘high’) are poorly distinguished in the f2 forecast category.
- Conen et al. [15] observed that “During most days of the year, emissions tend to be within the ‘low’ range, increasing to ‘medium’ or ‘high’ only after fertilizer applications, depending on soil temperature or WFPS limitations.”
- Recalling the data set from Figure 1, we note that as in [15], most emissions were in the ‘low’ observed range. The proportions of emissions in the ‘low’ (<10 g N2O-N ha−1 day−1), ‘medium’ (10-100 g N2O-N ha−1 day−1) and ‘high’ (>100 g N2O-N ha−1 day−1) observed ranges were ≈0.68, ≈0.30 and ≈0.02, respectively.
5. Conclusions
Acknowledgments
References
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Topp, C.F.E.; Wang, W.; Cloy, J.M.; Rees, R.M.; Hughes, G. Information Properties of Boundary Line Models for N2O Emissions from Agricultural Soils. Entropy 2013, 15, 972-987. https://doi.org/10.3390/e15030972
Topp CFE, Wang W, Cloy JM, Rees RM, Hughes G. Information Properties of Boundary Line Models for N2O Emissions from Agricultural Soils. Entropy. 2013; 15(3):972-987. https://doi.org/10.3390/e15030972
Chicago/Turabian StyleTopp, Cairistiona F.E., Weijin Wang, Joanna M. Cloy, Robert M. Rees, and Gareth Hughes. 2013. "Information Properties of Boundary Line Models for N2O Emissions from Agricultural Soils" Entropy 15, no. 3: 972-987. https://doi.org/10.3390/e15030972